License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ITP.2019.20
URN: urn:nbn:de:0030-drops-110754
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/11075/
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Haslbeck, Maximilian P. L. ; Lammich, Peter

Refinement with Time - Refining the Run-Time of Algorithms in Isabelle/HOL

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LIPIcs-ITP-2019-20.pdf (0.5 MB)

Abstract

Separation Logic with Time Credits is a well established method to formally verify the correctness and run-time of algorithms, which has been applied to various medium-sized use-cases. Refinement is a technique in program verification that makes software projects of larger scale manageable.
Combining these two techniques for the first time, we present a methodology for verifying the functional correctness and the run-time analysis of algorithms in a modular way. We use it to verify Kruskal's minimum spanning tree algorithm and the Edmonds - Karp algorithm for network flow.
An adaptation of the Isabelle Refinement Framework [Lammich and Tuerk, 2012] enables us to specify the functional result and the run-time behaviour of abstract algorithms which can be refined to more concrete algorithms. From these, executable imperative code can be synthesized by an extension of the Sepref tool [Lammich, 2015], preserving correctness and the run-time bounds of the abstract algorithm.

BibTeX - Entry

@InProceedings{haslbeck_et_al:LIPIcs:2019:11075,
  author =	{Maximilian P. L. Haslbeck and Peter Lammich},
  title =	{{Refinement with Time - Refining the Run-Time of Algorithms in Isabelle/HOL}},
  booktitle =	{10th International Conference on Interactive Theorem Proving (ITP 2019)},
  pages =	{20:1--20:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-122-1},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{141},
  editor =	{John Harrison and John O'Leary and Andrew Tolmach},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/11075},
  URN =		{urn:nbn:de:0030-drops-110754},
  doi =		{10.4230/LIPIcs.ITP.2019.20},
  annote =	{Keywords: Isabelle, Time Complexity Analysis, Separation Logic, Program Verification, Refinement, Run Time, Algorithms}
}

Keywords: Isabelle, Time Complexity Analysis, Separation Logic, Program Verification, Refinement, Run Time, Algorithms
Collection: 10th International Conference on Interactive Theorem Proving (ITP 2019)
Issue Date: 2019
Date of publication: 05.09.2019
Supplementary Material: The formalization described in this paper is available at https://www21.in.tum.de/~haslbema/Sepreftime.

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